Problem: 4 people can paint 6 walls in 31 minutes. How many minutes will it take for 5 people to paint 8 walls? Round to the nearest minute.
Explanation: We know the following about the number of walls $w$ painted by $p$ people in $t$ minutes at a constant rate $r$ $w = r \cdot t \cdot p$ $\begin{align*}w &= 6\text{ walls}\\ p &= 4\text{ people}\\ t &= 31\text{ minutes}\end{align*}$ Substituting known values and solving for $r$ $r = \dfrac{w}{t \cdot p}= \dfrac{6}{31 \cdot 4} = \dfrac{3}{62}\text{ walls painted per minute per person}$ We can now calculate the amount of time to paint 8 walls with 5 people. $t = \dfrac{w}{r \cdot p} = \dfrac{8}{\dfrac{3}{62} \cdot 5} = \dfrac{8}{\dfrac{15}{62}} = \dfrac{496}{15}\text{ minutes}$ $= 33 \dfrac{1}{15}\text{ minutes}$ Round to the nearest minute: $t = 33\text{ minutes}$